Series and other data related to the fiveparticle contribution χ^{(5)} to the square lattice Ising model susceptibility.
First a bit of notation. The `natural' variables are s=sinh(2J/kT) and w=s/(2(1+s^{2}))
Some exact results for nparticle contributions to the susceptibility
χ^{(1)} = 2w/(14w)  
ODE for χ^{(3)} in variable w.  
First column is the order k of the derivative, the second column is j and the third column is the j'th coefficient p_{k,j} in the polynomial P_{k}(w) multiplying the k'th derivative.  
ODE for χ^{(5)} in variable w mod the prime 32749.  
For χ^{(5)} we express the solution in terms of a linear ODE with polynomial coefficients but using the diffential operator (wd/dw). The solution is of order n=56 with the degree of the polynomials equal 129. The data is organised as a list of lists with the first list being the coefficients of P_{n}(w), the second list being the coefficients of P_{n1}(w) etc. etc. and the last list is the coefficients of P_{0}(w)  
Some exact series mod various primes.

For the prime 32749 the series has some 10000 terms
while for the remaining primes the series has some 5600 terms.
Series for χ^{(3)} in w mod the primes: 32749 32719 32717 32713 
Series for χ^{(5)} in w mod the primes: 32749 32719 32717 32713 
Some exact results for factors occuring in the order 29 differential operator L_{29} annihilating the series Φ^{(5)}=χ^{(5)}χ^{(3)}/2+χ^{(1)}/120

First we have the operator L_{11} in exact arithmetic.
This operator has the factorization:
The multiplications are done as differential operators and the addition is the direct sum of operators.
In terms of commands from the Maple package DEtools we have:
Next we have the operator L_{5} mod 32749. This is the minimal order ODE for this operator.
A solution to this ODE is given by
where E and K denote the complete elliptic integrals
while P_{4i,i} are polynomials in w with coefficients known modulo the prime 32749 and of degree 200, 202, 204, 204 and 204, respectively. Click here to download these polynomials .
Here we have the operator L_{13} mod 32749.
This is a nonminimal order ODE (order 19) for this operator.
In our paper J. Phys A 43 195205 (2010) we calculated the ODE in exact arithmetic. Below are some of main results.
Exact χ^{(5)} to order 8000, Exact L_{29} operator, Exact L_{24} operator, Exact L_{12}(right) operator, and sKE polynomials.
Exact L_{11} operator and `reduced' L_{13} polynomials Q_{k}. The polynomials occuring in L_{13} are P_{k}=Q_{k}*PA^{k}, where PA is the apparent polynomial of L_{11}
Since publication one of us (Bernie Nickel) has found several exact relations between the constants at the ferromagnetic point given in the arrays C_{0} and C_{1} of equation (B.4). These relations can be found here